The Social Graph of a Famous Mathematician

Above is the social graph [a.k.a. social network map] of Paul Erdõs. He was an expert in the mathematics of networks. Erdõs practiced what he preached -- he was a weaver of social networks and thus a builder of social capital.

Erdõs was known for traveling
the world and collaborating with mathematicians on problems and proofs
he found interesting. He would actually live with his collaborators for a week or two while they worked out the proofs. Then he would travel on to the next collaboration. Many scientific papers resulted from these intense
face-to-face collaborations. Erdõs had 507 co-authors, some of
whom collaborated with each other. Erdõs's partnerships exposed
the social structure of scientific discovery. An excellent mathematical analysis -- Evolution of the social network of scientific collaborations[PDF] -- is available from Laszlo Barabasi and colleagues.

These collaborations became so famous that soon mathematicians
were keeping track of their Erdõs Numbers. If you co-authored an
article with Erdõs you have a number of 1, if you co-authored a
paper with one of his direct collaborators you have an Erdõs Number
of 2, and so on. It has become very prestigious in the mathematics community
to have a low Erdõs Number. Dr. Jerry Grossman maintains a data
repository of Erdõs numbers and collaborators -- The
Erdõs Number Project -- from which I constructed the collaborator
graph.

Experts have long argued about the optimal structure of
a person's professional network. Some say that a dense, cohesive network
brings more social capital, while others argue that a sparse, radial network,
one that provides opportunities for innovation and entrepreneurial activity,
equates to greater social capital. Erdõs's network shows both patterns
-- a densely connected core along with loosely coupled radial branches
reaching out from the core. According to Ron Burt -- a
leading expert on social capital -- this structure may be the optimal pattern for success.
According to Burt, radial ties reach diverse information and knowledge
to create value, while the dense, trusted ties deliver value
in discovered opportunities. For a complete analysis read Burt's seminal
work -- The
Network Structure of Social Capital[PDF].